In a situation frequently encountered in practical applications, the force transducer used for the application is already under a high initial load which is not the target of the measurement. The force to be measured is actually a very small superimposed one.

Typical application examples:

  • Force washers are pre-stressed under bolts and yet they need to record extremely small forces.
  • Sensors which are clamped in place under considerable force must detect the slightest application of force for monitoring tasks.

In this article we present the advantages of piezoelectric sensors and force sensors based on strain gauges with reference to some applications that will be described.

Advantages of piezoelectric measurement technology

Piezoelectric sensors generate an electrical charge when a force is applied. The diagram above illustrates the operating principle.

Charges are generated proportionally to the force. The unit of measure for the charge is pC (10-12 Coulombs, which is equivalent to a charge of 3.12 * 10-6 elementary charges).

Sensors that use quartz as the piezoelectric sensor material exhibit a sensitivity of about 4.3 pC/N. This means that if a force of one Newton is applied to the sensor, a charge of 4.3 pC is produced. Some sensors use gallium phosphate as the piezoelectric crystal. The advantage is that twice the sensitivity can be achieved in this way. Twice as much charge is produced by the same force. The charges are directed to a charge amplifier, which converts the signal into a 0...10 V signal.

The advantage of this technology is that the sensitivity of the sensor remains the same regardless of the nominal (rated) force, assuming the same material.A very large sensor can also be used to measure a very small force. Another reason to prefer this technology is that charges can be physically set to zero. A short circuit can be used to produce a charge of zero pC on the input when the sensor is loaded by a force (in our example pre-stress).

In this situation the charge amplifier can be set to a higher sensitivity so that the measuring range corresponds to the force being measured. The pre-stress is not relevant. It makes no difference for the resolution and accuracy of the measurement whether a piezoelectric sensor is operated under initial load or with none at all. It is always possible to bring the input of the charge amplifier to zero by using the RESET function.

Piezoelectric sensor working under an initial load: After the initial load is applied the measuring chain is brought to zero by a reset. Now the charge amplifier can be operated in a very well adjusted (smaller) measuring range.


A force washer is installed under a bolt. The object is to measure a tensile force acting on the screw connection. First the pre-stress force is applied. The pre-stress force can also be determined by measuring it with the force washer itself. A zero balance for the measuring chain can be performed by triggering a RESET on the charge amplifier. Then there is no charge on the input. Now the charge amplifier can be set to any measuring range. Even very small forces can now be measured reliably.

Please note:

  • This measurement is especially simple with modern digital charge amplifiers such as the CMD600, which can be set to any measuring range.
  • In the example shown here the measurement is in the force shunt. A calibration in the installation situation is required before forces can be measured quantitatively. For more information read the article 'Installation of force transducers'.
  • Piezoelectric sensors are always subject to drift. This makes it necessary to bring them to zero cyclically or use a high-pass filter. If neither option is available, strain gauge-based sensors must be used.

Advantages of strain gauge-based technology

Sensors based on strain gauges (SG) work according to the following principle:

  • A force is applied to a spring element so that the spring element is minimally deformed.
  • Strain gauges are glued on at suitable points to convert the deformation into a change in electrical resistance.
  • With adept wiring (a Wheatstone bridge circuit) and a voltage supply, this change in resistance can ultimately be converted into a measurable voltage.

The advantage of SG sensors is that they can be electrically calibrated with many different characteristic quantities, such as the temperature coefficient of zero point and sensitivity, the effect of the bending moment and also linearity. Depending on the requirement, unparalleled accuracy can be achieved with this technology.

The output signal of a sensor of this type is a voltage. The voltage always depends on the excitation voltage that supplies the sensor. Not taking into account the output signals resulting from error effects (temperatures, parasitic loads, etc.), there remain two parameters determining the overall signal:

  • The "relative zero signal error" describes the output signal of an unloaded transducer.
  • The force applied on the sensor is converted into a measurable electrical output signal as described above.

If a zero balance is performed in the software or on a measuring bridge amplifier, it is always an addition or subtraction of the two voltages described above. This can usually be done through computation in the amplifier or software. This can usually be done through computation in the amplifier or software. The output voltage of the measuring chain remains unchanged. The measuring range of the sensor must be selected to correspond to the entire force, thus the applied pre-stress and the force to be measured.

In the example above, monitoring a steel cable that supports an electrical line, the changes in the tensioning force are very small compared to the base stress. Since a small signal change in a wide measuring range needs to be acquired, it is understandable that very high resolution is therefore required for the measurement signal. The errors in the force measurement chain must also be significantly less than the changes in force that are being measured.

Influence quantities, especially those related to the full scale value in measurement uncertainty observations, play a major role here. For more detailed information on this topic read the article 'High accuracy is high efficiency: Why particularly accurate force transducers enable new application areas'. A low effect of temperature on the zero signals, a small linearity error and low creep are very important for reliable measurement results. Unlike the measurement of very small forces using sensors with a high nominal (rated) force, however, the temperature coefficient of sensitivity is an important consideration in this application. As explained above, the loaded sensor generates an output voltage, even if it is not displayed because the amplifier has been zeroed. If the sensitivity of the sensor changes due to the effect of temperature, this directly impacts on the output signal. This impact increases, when the constantly applied initial load grows - in our example, high rope tension.

Please note:

  • Radially symmetrical shear force transducers are very precise and rugged and have proven effective in many cases, especially if the measurement is performed at changing temperatures. Sensors of this type exhibit very little creep (250 ppm in 30 min) and especially very few temperature errors. The new C10 compressive force transducer has a temperature dependency of zero point of just 75 ppm/10K. The U10M force transducer achieves similar excellent characteristic values.
  • S-shaped force transducers (S2M, S9M) are worth considering for small forces. They also work very precisely. Unlike radially symmetrical shear force transducers, however, restrictions in dynamic behavior must be accepted.
  • Because SG sensors are not subject to drift, there is no alternative to strain gauge-based technology if a cyclic RESET or use of high-pass filters is not possible.


Measuring small forces or small changes in forces places high requirements on the accuracy of sensors.

The piezoelectric principle offers the advantage that the measuring range of the charge amplifier can be selected so that it fits the small force to be measured exactly.

SG-based sensors are now available with extremely high accuracy. Low temperature effects, small linearity deviations and outstanding absence of drift based on the working principle make them the first choice for all processes where cyclic zeroing is not possible.
